Preheat oven to 350°F. Spray the cavities of the mini bundt pan with non-stick spray. Set aside. (See Tips 3 and 4)
Cream butter, brown sugar, and granulated sugar with an electric mixer on high speed until light and creamy, about two minutes. Add eggs, one at a time, beating well after each addition, about one minute per egg. Scrape down the sides of the bowl.
Add buttermilk, vanilla extract, baking soda, salt, cinnamon, nutmeg, and allspice. Beat until well combined, about one minute. Scrape down the sides of the bowl. (See Tip 5)
Add the flour; beat on low just until combined. Fold in the apples.
Add the batter to the prepared mini bundt pan using a 1 ¾-inch scoop, with the batter level in the scoop.
Bake in the preheated 350°F oven for 18 to 20 minutes, or untl the sides begin to pull away from the pan and a toothpick inserted into the center comes out clean.
Remove from the oven to a wire rack. Let cool in the pan for five minutes. Remove the bundtinis from the pan and let cool completely on a wire rack.